Further robust stability analysis for uncertain Takagi-Sugeno fuzzy systems with time-varying delay via relaxed integral inequality.

*(English)*Zbl 1432.93269Summary: This paper focuses on robust stability analysis for uncertain Takagi-Sugeno fuzzy systems with time-varying delays. Two delay-product-type terms are introduced for constructing a new Lyapunov-Krasovskii functional, which contains more information of time-varying delay. And a novel relaxed integral inequality is applied to estimate the derivative of LKF for achieving reduction of estimation gap. As a result, several further robust stability criteria with less conservativeness are proposed. Finally, three numerical examples and an application to control of a truck-trailer are provided to show the effectiveness and advantages of the presented methods.

##### MSC:

93D09 | Robust stability |

93C42 | Fuzzy control/observation systems |

93C41 | Control/observation systems with incomplete information |

93C43 | Delay control/observation systems |

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